The Algebra of \"Everything\" by Rick Lockyer

On Edwin's point about changing minds, you have had an effect on changing my mind, although the preferred phrasing is of course, refined my thinking (if not quite in the way you may have intended). Observational physics naturally divides into the world outside of hadrons, and the inner hadron world. In the outer world there is space and time with associated inner particle symmetries spin (S3) and particle/anti-particle, isospin symmetry (S3) and hypercharge symmetry (S1), but no colour symmetry, giving an 8 dimensional outer world of most observations in physics (I think this was the point that Edwin was making).

In my case, this outer world is of a cyclical (S1) closed universe (S3) with electroweak base-space (S4) forming a product space. Here, gravity in S3 is by curvature and the particle forces of S4 by torsion, which are incompatible to be embedded in the same space. BUT in a local (vicinity) theory it may be possible to construct a torsion based view of gravity and so combine S3 and S4 into S7 to give your suggested Octonion Relativity covering the outer hadron world.

Joy's 2 particle correlation analysis for observables in the outer hadron world could be viewed as reaching the same conclusion. In the Standard Model, the electroweak charges are chiral and so spin orientation in S3 is related to isospin orientation in its S3, and hypercharge S1. The conclusion that correlations are due to the embedding of these spaces in S7 requires a flat parallelised sphere with torsion. There are 3 spaces here (physical space, symmetry space, measurement space) and whereas I deal with the first 2, Joy effectively deals with the second 2 - so direct comparison is a bit confusing. This is made worse in my GR model by compactified physical spaces being identified with symmetry spaces (as in Kaluza-Klein theories) - the physical scale factor between the 2 is the charge coupling constant.

In the inner hadron world there is also colour, which is not correlated with spin or the electroweak charges. This implies that Joy's correlation analysis for 2 colour observables (C, D) can be applied independently of the spin/electroweak observables (A, B) as there is no correlation between (A, B) and (C, D). The conclusion is the parallelised spheres S3 or S7, neither of which obviously squares with the Standard Model colour group SU(3). S7 isn't a group space, but S3 is - of SO(3). 2 particle correlation (the 2 quarks inside a meson) of an S3 colour space would yield S3 in Joy's analysis, whereas 3 particle correlation (a baryon) would yield the S7 result.

For your point of view, the inner hadron world yields a second independent occurrence of an S7 measurement space, as opposed to just the one in the outer hadron world. These inner and outer S7 occurrences could have the look of being mathematically dual, but as the references of Jens say that the E8 lattice is self-dual that may be a road to nowhere.

So you have persuaded me in principle, that in the outer hadron world it may be possible to construct a form of Octonion Relativity - which would necessarily be flat and not involve curvature - that could describe the measurement space of observables and particle symmetries. However, the spaces would not be physical spaces in the sense meant by Einstein. This would be apparent in particles having to be added by hand, and the theory not being extendable to the whole universe (that would be an invalid induction from a local vicinity theory). The corresponding physical theory for such an observational theory could of course be mine. I'm sticking with Albert on his concept of physicality and specifically a physical GR, as if I abandon this point then I would no longer consider myself a physicist.

There are 3 different types of space (physical, symmetry, measurement) and we may be confusing between them. We (me, you, Joy, Jens, ...) may not actually be handling separate beasts, but different parts of the same elephant.

Regards,

Michael

always weak and furthemore too much focus on 2D.In fact you are not competent for this play.Buy people or please increase your team because there it is too easy. I d say even that it is time that you really kill me.Because I don't understand how you can support all this teaching from me. In fact probably that you have still more hate against me.It is logic for this kind of persons. Aahahah even your strategy is weak, it is easy to find the holes and errors.ahahah a lesson, who gives a lesson to who band of comics. in all cneters of interest I eat your sciences at my breakfast.I am understanding that my arrogance increases your hate, but frankly I have pity.An advice don't speak about that inside the global sciences community.you know it exists the trues and the falses. But I understand your comportment.In fact it is logic in this time of crisis. You fear to loose investments or to be less credible.But you know it is the life. The strategists even with all the tools and with a lot of friends cannot win against he message of God.Am I Crazy? Yes , it is evident. I am insisting you know dear bad team, your only one solution is to be murders. And what ? you think what ? my universal faith is so above yours that I am laughing in fact. The revolution spherization has already began. You do not imagine the number of persons knowing my theory. and it is a begining. Alone with an old pc and without net protection.and you with your strategy of superimposings with the SOA adapted for specific selected strategists. Incredible no, even like that I give you the informations and I so optimize your quantum systems. Ahahaha I have the syndrom of the savor,I beleive that I am the elected ahahah wait I see spheres everywhere and you know what they speak me, I am not alone in my head band of comics.

ps please the team is weak,please dear directors of this team, buy and pay others people, thay have not really good discussions with relevance.Even the entropy they do not know, even the gravitation they do not understand. Really it is frustrating to see these weak posts.You have not better competitors please ? because they repeat always the same.

wait, they are going to invenbt a time machine to travel towards the aether. :)

wawww impressing their maths ahahah so incredible that even God is without words ahahah wait he says me, Steve, my son, they are simply not aware of the truth, keep faith my son.....

amen

Regards

ahahah weak like always, make surf really. It is cool the people making surf.ahahah me I like soccer and I play well. I am going to create a song in honor of your bad team ahahah and hop on the net.

ahahah the poor strategists, the poor thinkers. Mr Witten , forget these pseudos, it is better for the credibility at my humble opinion. But it is just a suggestion of course.

octonions ahahaha and surf ahahah and the toe ahahah wawww impressing the strategy, you are so strong wawwww.ahahah the maths they say. if your maths are correct , me I am the queen of England.

Regards

The maths are the sister of physics.They dance together. It is time to stop confounding things. A real pity for your team.Edwin, you know what? you have not a consciousness you and your friends, so don't speak about things totally unknown.You are neither scien,tists nor generalists.Don't teach but learn dear badteam. You do not merit it !!!

You are really not skilling, just a little for the strategy, the rest frankly Let me laugh.

MIT wake up please , what are these pseudos ???Jonathan, change of job or make surf, I don't know me. You think what? that New york is to you or what? It is the country of the freedom dude. And what you fear for your credibility poor strategist. You are right, so kill me poor dude. But I am persuaded that you cannot make it alone. Buy people dude and pray if you have faith of course.

Delete now Brendan , just like that I can thinking that I am not checked on this platform. ahahah ironical your strategy since the begining with the two books. Ironical.

Regards

Rick,

I have closed geometric formula for Planck's constant, Weinberg angle, the coupling constants - including the Higgs coupling - in terms of the fundamental constants G, c and the compactification scale. When combined with the charge eigenvalues these give quantitative values for *all* the particles known to exist - and they agree to the level of experimental error. The quantitative calculation of the particle masses is proven to encounter the issue of mathematical incompleteness. This can be by-passed by changing maths represenation because maths is not the same as physics - this change *is* the origin of Quantum Field Theory.

My position is as quantitative as it is mathematically possible to be. The barrier to greater quantitative results is mathematical incompleteness - maths stands in the way of physics, but that maths barrier can be overcome by using experimental results. It has been said many times before, and it is still true: the map (maths) is not the territory (physics).

Michael

Hello crazy planet,

:) REVOLUTION SPHERIZATION OF HIGH SPHERES :)

without real universal meaning.

You are not really mathematicians.At my knowledge the mathematicians help to build for example a machine, an engeniering, or a technology. You build what with your octonionic strings of extradimensions ?

Answer: nothing.

In fact you do not respect the universal domeins and its limits. You utilize an ocean of pseudo theorems mixed with some rational.How can you have a correct conclusion. The probelm in fact is simple. You confound the computing 2d and the 3D realism.Furthermore you integrate bizare, you derivate without determinism, you substitute without sense and reason, ...in fact your maths do not improve, they are just lost these maths in an ocean of physical determinism.

and you speak about G,c and h. is it a circus from false mathematicians? if yes it is time to learn the real foundamental books you know.

Insist now, make the obliged strategist, delete, arrange like you want, make what you want dear badteam. It is not a problem for me. Mr Wilszec, what is this circus??? Mr Witten,you agree with this you ? I am persuaded that no.

Sad is a weak word.Just due to their vanity and the jealousy and the hate and the money.

Ironical.

signed the crazy spherical Jedi

Rick,

As a fellow physicist you know that the line between Maths and Physics was drawn by Galileo - Physics only existed after he set the experimental standard of applying a mathematical theory to reality. It's not my definition of Physics, it's Galileo's. Every theory starts as *just* a mathematical theory until experimentally verified and shown not to contradict known experimental results. Reproducing known theories by different means - which both you and I have done - meets the Galilean standard of Physics as the known experimental results are entailed (question answered).

In the Standard Model, the spectrum of particles and their coupling constants are added by hand from experimental results. Dimensional compactification defines a whole class of mathematical theories that seek to derive the particle coupling constants from the GR constants and a compactification scale. The 11D GR theory referenced in my essay is one of this class of theory and succeeds by *deriving* the full spectrum of particles so that they do not have to be added by hand - this is not present in the Standard Model or any associated principles. The GR scenario is uniquely defined mathematically by the occurrence of the spheres S0, S1, S3, S7 as physical manifolds and this is directly linked to the successful reproduction of known physics without any additional features that conflict with known physics. This includes the derivation of the correct Standard Model Lagrangian and QFT. These characteristics *are* unique.

The acknowledgement of "if and only if" in Godel's mathematical incompleteness is PRECISELY my point. It is conditional on integers, which is the case in classical physics for particle numbers. The calculation of the rest mass of the particles derived in 11D GR as topological defects is subject to Godel's mathematical incompleteness because of this "if and only if" condition. A mathematician would be stumped at this point, but as physicists who know that maths is just a formal language for describing reality, we are free to drop the "if and only if" condition of strictly using integers to denote particle numbers and switch to real numbers instead - the wave-function - mathematical incompleteness then vanishes. If you trace the mathematical consequences of this shift in the theory, you find that it is of the form of quantum theory. Hence, QT is not fundamental because I can derive it!

This implies that mathematical incompleteness is not so much a red herring, but the elephant in the room.

Michael

In the film spherewars by Spielberg,Steve the young Jedi has found an important thing, the force is with him. But the empire of the bad is there. The son of Yoda is his friend.

About the post:here is my humble point of vue of spherewalker.

all false !!! mike badteam ,the octonionic obliged comportment will not change the algorythms, deterministic. The aim is not to superimpose the maths without a real universal domain. In fact it is a good tool for computing.

you think what ? that you are going to insert balls now.Let me laugh band of comics.You are not skilling to ponder this kind of works.So what is the probelm. Mr Wilcszec is an universalist. Mr Tegmark also, Mr Guth also, Mr Penrose also, Mr Hawking also,Mr Witten also.so why you insist on the pseudo works,you do not respect the real searchers, you just imply strategy of strategical steal. In fact you know what ? I beleive that you do not permit the truths.Just because you confound a lot of things.It is simply an unconsciousness comportment.In fact you think that you are right. But no, there are a lot of probelms.

and you,Mr Witten , are you going to continue to act like that ? You fear for your 11d or what ??? If some persons of your team utilize several roads for the confusions about ball and sphere, frankly it is sad.and But perhaps that you do not know that they act like that?

Spherically yours

Rick,

I really had in mind, the so-called "pretty" maths of super-symmetry and string theory, whose "prettiness" has been used as justification for pursuing what has proven to be a pointless course for decades.

I have a preference for the geometric view of the same algebra, as it conceptually gives a big picture view which can guide the choice of direction to go in, and this is what the S7 geometric view of the octonions has done for me. An algebraic view is necessary to guide individual steps, and to conceptually check you don't step in anything nasty ;-), but can it really provide the big picture view of where to go next?

Your response on Godel's incompleteness strikes me as the exact opposite of what I meant. The classical physics theory over the integers is provably mathematically incomplete; the unbridgeable category divide between integer particle numbers and waves makes reaching a wave property from integer particles impossible in classical physics. So when a particle has a wave property, the classical physics theory is scientifically incomplete in the experimental sense that there-exists an observation that cannot be derived within classical physics. It is this specific sense of scientific completeness which can be addressed by dropping the "if and only if" condition of describing particle numbers by integers and instead use a real valued wave-function that incorporates the undecidable wave feature. The result is quantum theory - surely a very un-herring-like outcome?

Deeper philosophical points about "completeness" don't arise for this restricted experimental sense of scientific completeness; I use this term precisely so as to avoid the general notion of "completeness" which seems so vague you wouldn't know it if you found it.

No Space Shuttles out my window, just a buzzard if I'm lucky ;-)

Michael

PS. In my Sept 25 reply to Jonathan I give a view of Joy's frameworks in terms of topological mappings and particles as monopoles if your interested.

Hello Rick,

While the story goes that the Octonions are the weird and crazy old uncle whom everyone would like to hide away in their closet or attic; that is only partly true, and misses the point somewhat. Instead; the octonions are like the wealthy and eccentric old uncle, who almost nobody else in the family associates with, because they are intimidated by his freedom and power. Of course; the rest of the family is jealous, but they would never admit it, because then they would end up feeling a little less powerful themselves.

But we would all be a whole lot less wealthy, if it were not for the Octonions - which are the great granddaddy of all the other number types. However; the wonderful properties of those amazing octonions assure that the rest of the family emerges and persists as well. I rated your essay highly, because I believe in what you are saying - and that you said it well. Of course; I fully understand that you can't talk meaningfully about your subject without getting too technical sometimes, which you did, but so it goes.

All the Best,

Jonathan

Hmm,

Thinking on the above comment; I imagine you could make a detailed storyline out of it - where, for example, the rest of the family will only approach uncle Octonius in committees of three, but there is always a member of each committee in common. Such a dramatic approach might illustrate the kind of special respect the octonions demand. Just a thought.

But I like the idea of the Octonions being a wealthy and eccentric uncle (who knows untold secrets) better than a weird and crazy one, any day.

All the Best,

Jonathan

To continue;

Good old Uncle Octonius was one crafty old genius. The family insisted that the only way anyone in the family could be trusted to meet with him is if they went in committees of three. And of course; he insisted that - in order to be fair - there must be one member in common each time they send a committee. But how did he know that there would be seven committees? That crafty old guy must have planned it that way.

Of course; the committees are called quaternions - which is short for "It's our turn again." Anyhow; I'm just thinking out loud on your page.

All the Best,

Jonathan

If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is [math]R_1 [/math] and [math]N_1 [/math] was the quantity of people which gave you ratings. Then you have [math]S_1=R_1 N_1 [/math] of points. After it anyone give you [math]dS [/math] of points so you have [math]S_2=S_1+ dS [/math] of points and [math]N_2=N_1+1 [/math] is the common quantity of the people which gave you ratings. At the same time you will have [math]S_2=R_2 N_2 [/math] of points. From here, if you want to be R2 > R1 there must be: [math]S_2/ N_2>S_1/ N_1 [/math] or [math] (S_1+ dS) / (N_1+1) >S_1/ N_1 [/math] or [math] dS >S_1/ N_1 =R_1[/math] In other words if you want to increase rating of anyone you must give him more points [math]dS [/math] then the participant`s rating [math]R_1 [/math] was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

Sergey Fedosin

Mr Lockyer,

a very interesting essay. I remember a few years ago I was looking for math that would allow the multidimensional nature of space to be expressed with ease. I wish I had found Octonion Algebra then, but all I saw was quaternions. I imagine how hard it was to pack it all in 9 pages -- well done! I hope your essay will get the recognition it deserves.